Could Obamacare eligibility stymie comprehensive immigration changes? House negotiators, at least, are working to mitigate this potential hurdle.

The bipartisan House immigration working group is exploring legislative options to prevent the millions of illegal immigrant residents who would be legalized under a comprehensive overhaul from becoming immediately eligible for health care benefits under the Affordable Care Act, sources confirm. The goal is to keep the cost of the overhaul down and prevent the kind of high Congressional Budget Office score that might even scare away Democrats, never mind Republicans.

“We are concerned about the overall cost, and that is a concern on both sides of the aisle,” a GOP aide familiar with the House negotiations told CQ Roll Call on Wednesday.

Overhaul supporters monitoring the Senate fear that Democrats who might favor immediate Obamacare eligibility for newly legalized immigrants could prevail on New York Sen. Charles E. Schumer and other Democratic negotiators. Proposing to allow former undocumented immigrants such access to the Affordable Care Act could cause a political uproar on the right, costing any bill the GOP support it needs to clear both chambers. And, that's before President Barack Obama's opinion on this matter is considered.

In the House, one solution under discussion is a statutory change to the health care overhaul.

One House member privy to the House negotiations, and open to supporting the overhaul, said that immigration overhaul legislation could propose changing the legal requirement for Obamacare eligibility from “in the country legally” to “legal permanent resident.” Under this approach, newly legalized immigrants would not be eligible for federal benefits in general, including those provided under the Affordable Care Act, for a period of seven to 10 years after legalization.

The overhaul might even require newly legalized immigrants to obtain health insurance as a condition of moving beyond probationary status, according to one GOP operative working on behalf of the pro-overhaul forces. Preventing illegal immigrants from accessing Obamacare was a political sticking point during the debate over the president’s landmark health care overhaul bill. The GOP operative said how to address Obamacare in the immigration overhaul legislation is similarly a political “thicket.”

The Republican aide familiar with the House negotiations suggested that a solution that does not involve amending the Affordable Care Act is the preferred route to addressing this problem. And sources said that, at least in the House, the Democrats who are negotiating the immigration compromise are on board with the end goal of preventing immediate health care law eligibility, if for no other reason than they recognize that a high price tag could kill an overhaul.